I am coming to linguistics from a completely non-linguistic background; I was a mathematician. Next year I will start taking some serious (Master's level) linguistics courses and I would like to have considerable background in the topics that will be covered so that I can be as best prepared as possible. The courses will be on syntax, semantics and phonetics/phonology. Below, I am providing brief descriptions of the courses:
Syntactic Analysis: This course is an introduction to basic goals and methods of current syntactic theory through a detailed analysis of a range of phenomena, with emphasis on argumentation and empirical justification. Major topics include phrase structure and constituency, selection and subcategorization, argument structure, case, voice, expletives, and raising and control structures.
Semantics and Pragmatics: This is the first in a two-course sequence designed to provide a foundation in the scientific study of all aspects of linguistic meaning. The first quarter focuses primarily on pragmatics: those aspects of meaning that arise from the way that speakers put language to use, rather than through the formal properties of the linguistic system itself, which is the domain of semantics. However, a central goal of the course will be to begin to develop an understanding of the relation between pragmatics and semantics, by exploring empirical phenomena in which contextual and conventional aspects of meaning interact in complex but regular and well-defined ways, and by learning analytical techniques that allow us to tease these two aspects of linguistics meaning apart.
Phonological Analysis: This course introduces cross-linguistic phonological phenomena and methods of analysis through an in-depth examination of fundamental notions that transcend differences between theoretical approaches: contrast, neutralization, natural classes, distinctive features, and basic non-linear phonological processes (e.g., assimilation, harmony, dissimilation).
I would be most grateful if you could suggest textbooks (and, more generally, resources — including, but not limited to, lecture notes, websites, software) that would help me get a good grasp of this material. Textbooks that have become mainstream in the postgraduate study of these subjects will be especially helpful!